6 ms·

What’s special about it?

klodolph 2y ago
They’re trying to solve various issues with harmony. You want to pick a set of notes that produce good harmonies with each other, but you don’t want to pick too many notes. If you “fudge” some notes, which compromises the harmony, you can keep a small set of notes in the octave (like twelve!), and if you’re careful about it, the music will still sound consonant / harmonious when it is supposed to sound that way. Historically, the older systems were some derivation of Pythagorean or just intonation, which are generated from small integer ratios like 3:2, 4:3, 5:4. If you continue building a tuning system out of these integer ratios, you get weird ratios like 81:80 (syntonic comma) or 531441:524288 (Pythagorean comma); you can then choose to include these ratios in your tuning system (too complicated), stop before you reach them (too simple), or divide up the ratios and distribute them in other parts of your scale. This last approach is called “musical temperament”. https://en.wikipedia.org/wiki/Musical_temperament https://en.wikipedia.org/wiki/Musical_temperament Werkmeister devised a set of musical temperaments in the late 1600s. Alternative temperaments include mean-tone temperament (various flavors) and equal temperament. Mean-tone temperament divides the commas equally apart parts of the octave. Equal temperament divides the commas equally across the entire octave. Werkmeister temperaments divide the commas unequally. This results in some intervals which sound more consonant and some intervals which sound more dissonant, relative to equal temperament. Unlike equal temperament, different keys will have different character. Just to illustrate a more concrete problem: systems which improve the fifth often require sacrificing the third. Pythagorean has exactly perfect fifths but the thirds are not so good. Quarter-comma meantone goes the opposite direction and gives you exactly just thirds, but the fifths are not so good. Equal temperament is between the two, but much closer to Pythagorean. If you want to play with it immediately, and you have Logic Pro installed, you can go menu diving into the tuning settings for your project. Other DAWs too. Various synthesizers also have Werkmeister buried in the menus—some brands more than others (I know Yamaha has had them for ages).
- brudgers 2y ago
  The manual for my Yamaha EW20 Windjamm’r is where I stumbled upon it. I find non-12TET temperaments anthropologically interesting in the context of European classical music culture…e.g. what does the exalted status of “perfect pitch” imply?
  - klodolph 2y ago
    “Perfect pitch” or “perfect interval”? Someone with perfect pitch can tell what note you are playing just by listening to that note in isolation. Most people can’t do that. “Absolute pitch” is probably a better name, but it’s usually called “perfect pitch”. Perfect intervals are the intervals which don’t have a smaller and larger version of an interval with the same name. It’s nothing more than a naming convention for intervals. The 4th and 5th are perfect. So are the octave (8th) and unison (1). The other intervals (2nd, 3rd, 6th, and 7th), rather than being “perfect”, come in minor and major versions. Basically, every interval either has minor/major, or perfect. It’s a naming convention for intervals based on the western diatonic scale. Any interval which is smaller than minor/perfect is called “diminished”, and an interval which is larger than major/perfect is “augmented”. For example, C to Gb is a diminished fifth, and Ab to F# is an augmented sixth. Which number you use to name an interval is strictly based on the letter names of the note, ignoring sharps and flats.
    - brudgers 2y ago
      I used "perfect pitch" in the ordinary way ordinary people ordinarily use the phrase. Temperaments are interesting because the pitches (and intervals) in 12TET are different from the pitches (and intervals) in Mean Tone are different from the pitches (and intervals) in Werckmeister -- and within Werckmeister because Werkmeister made several temperaments. Never mind 31TET etc.
      - klodolph 2y ago
        > I used "perfect pitch" in the ordinary way ordinary people ordinarily use the phrase. I’m a little confused by what you are saying here, because most people who say “perfect pitch” mean that you can tell which note is being played in isolation. That’s what “perfect pitch” means to ordinary people, as far as I can tell. It’s something you have or don’t have. Like, “I have perfect pitch” or “I don’t have perfect pitch”. If you mean something other than that definition, maybe you could find some alternative way to express it because I don’t understand what meaning you are getting at. I’m not trying to be pedantic here, but “perfect pitch” is right there in the dictionary and it’s most commonly used to mean that you can recognize pitch without a reference, i.e., absolute pitch recognition.
TheOtherHobbes 2y ago
It's a different take on trying to set up the pitches on a piano/organ/synth keyboard so you can shift between keys and everything still sounds tuneful. Ideally you want exact numeric ratios between the various note combinations. (E.g. the frequency of a G should be 1.5 times the frequency of a C.) If you start with a C and set up perfect ratios, you get a smooth sound as long as you play in the key of C. But if you change key and move pitch patterns up and down the keyboard - transposition - the pitches will be off. Sometimes by a lot. So you have these different systems that try to approximate a solution in different ways. Modern Western music uses Equal Temperament, where the frequency ratio between notes is the same all the way up the keyboard (exactly the 12th root of 2.) This is super-simple and gives close-enough ratios that aren't quite exact but are very usable. The cost is a hint of sourness in some note combinations, but mostly we just hear those as movement within the sound. The older alternatives to Equal (mean tone, Werckmeister, Kirnberger, and others) smooth out the ratios more selectively. So some note combinations are less sour, others are more sour. They sound quite spicy if you're not used to them - somewhat out of tune (ironic...) but most people are so used to Equal Temperament anything else sounds exotic. So something like this is of historic interest. These tunings are sometimes used for authentic performances of very old ('early') music, and some old church organs were built with them. It's very rare to find them being used for effect in modern songs. (Does happen, but very unusual.) The best solution is dynamic tuning which takes into account the surrounding notes and shifts pitches a little up and down for the smoothest effect. Choirs and orchestras tend to do this anyway, but making it happen in software is a much harder problem.
- thih9 2y ago
  About software implementations of dynamic tuning - Logic Pro supports this, under the name “Hermode Tuning” https://support.apple.com/en-gb/guide/logicpro/lgcpa88a63e7/mac https://support.apple.com/en-gb/guide/logicpro/lgcpa88a63e7/... > Hermode Tuning automatically controls the tuning of electronic keyboard instruments (…). It retains the pitch relationship between keys and notes, while correcting the individual notes of electronic instruments, ensuring a high degree of tonal purity. This process makes up to 50 finely graded frequencies available per note, while retaining compatibility with the fixed tuning system of 12 notes per octave. Other DAWs have similar options, e.g. Cubase: https://www.steinberg.help/r/cubase-pro/13.0/en/cubase_nuendo/topics/midi_realtime_parameters_and_effects/midi_realtime_parameters_midi_modifiers_hermode_tuning_r.html https://www.steinberg.help/r/cubase-pro/13.0/en/cubase_nuend...

They’re trying to solve various issues with harmony. You want to pick a set of notes that produce good harmonies with each other, but you don’t want to pick too many notes. If you “fudge” some notes, which compromises the harmony, you can keep a small set of notes in the octave (like twelve!), and if you’re careful about it, the music will still sound consonant / harmonious when it is supposed to sound that way. Historically, the older systems were some derivation of Pythagorean or just intonation, which are generated from small integer ratios like 3:2, 4:3, 5:4. If you continue building a tuning system out of these integer ratios, you get weird ratios like 81:80 (syntonic comma) or 531441:524288 (Pythagorean comma); you can then choose to include these ratios in your tuning system (too complicated), stop before you reach them (too simple), or divide up the ratios and distribute them in other parts of your scale. This last approach is called “musical temperament”. https://en.wikipedia.org/wiki/Musical_temperament https://en.wikipedia.org/wiki/Musical_temperament Werkmeister devised a set of musical temperaments in the late 1600s. Alternative temperaments include mean-tone temperament (various flavors) and equal temperament. Mean-tone temperament divides the commas equally apart parts of the octave. Equal temperament divides the commas equally across the entire octave. Werkmeister temperaments divide the commas unequally. This results in some intervals which sound more consonant and some intervals which sound more dissonant, relative to equal temperament. Unlike equal temperament, different keys will have different character. Just to illustrate a more concrete problem: systems which improve the fifth often require sacrificing the third. Pythagorean has exactly perfect fifths but the thirds are not so good. Quarter-comma meantone goes the opposite direction and gives you exactly just thirds, but the fifths are not so good. Equal temperament is between the two, but much closer to Pythagorean. If you want to play with it immediately, and you have Logic Pro installed, you can go menu diving into the tuning settings for your project. Other DAWs too. Various synthesizers also have Werkmeister buried in the menus—some brands more than others (I know Yamaha has had them for ages).

brudgers 2y ago
The manual for my Yamaha EW20 Windjamm’r is where I stumbled upon it. I find non-12TET temperaments anthropologically interesting in the context of European classical music culture…e.g. what does the exalted status of “perfect pitch” imply?
- klodolph 2y ago
  “Perfect pitch” or “perfect interval”? Someone with perfect pitch can tell what note you are playing just by listening to that note in isolation. Most people can’t do that. “Absolute pitch” is probably a better name, but it’s usually called “perfect pitch”. Perfect intervals are the intervals which don’t have a smaller and larger version of an interval with the same name. It’s nothing more than a naming convention for intervals. The 4th and 5th are perfect. So are the octave (8th) and unison (1). The other intervals (2nd, 3rd, 6th, and 7th), rather than being “perfect”, come in minor and major versions. Basically, every interval either has minor/major, or perfect. It’s a naming convention for intervals based on the western diatonic scale. Any interval which is smaller than minor/perfect is called “diminished”, and an interval which is larger than major/perfect is “augmented”. For example, C to Gb is a diminished fifth, and Ab to F# is an augmented sixth. Which number you use to name an interval is strictly based on the letter names of the note, ignoring sharps and flats.
  - brudgers 2y ago
    I used "perfect pitch" in the ordinary way ordinary people ordinarily use the phrase. Temperaments are interesting because the pitches (and intervals) in 12TET are different from the pitches (and intervals) in Mean Tone are different from the pitches (and intervals) in Werckmeister -- and within Werckmeister because Werkmeister made several temperaments. Never mind 31TET etc.
    - klodolph 2y ago
      > I used "perfect pitch" in the ordinary way ordinary people ordinarily use the phrase. I’m a little confused by what you are saying here, because most people who say “perfect pitch” mean that you can tell which note is being played in isolation. That’s what “perfect pitch” means to ordinary people, as far as I can tell. It’s something you have or don’t have. Like, “I have perfect pitch” or “I don’t have perfect pitch”. If you mean something other than that definition, maybe you could find some alternative way to express it because I don’t understand what meaning you are getting at. I’m not trying to be pedantic here, but “perfect pitch” is right there in the dictionary and it’s most commonly used to mean that you can recognize pitch without a reference, i.e., absolute pitch recognition.

TheOtherHobbes 2y ago

It's a different take on trying to set up the pitches on a piano/organ/synth keyboard so you can shift between keys and everything still sounds tuneful. Ideally you want exact numeric ratios between the various note combinations. (E.g. the frequency of a G should be 1.5 times the frequency of a C.) If you start with a C and set up perfect ratios, you get a smooth sound as long as you play in the key of C. But if you change key and move pitch patterns up and down the keyboard - transposition - the pitches will be off. Sometimes by a lot. So you have these different systems that try to approximate a solution in different ways. Modern Western music uses Equal Temperament, where the frequency ratio between notes is the same all the way up the keyboard (exactly the 12th root of 2.) This is super-simple and gives close-enough ratios that aren't quite exact but are very usable. The cost is a hint of sourness in some note combinations, but mostly we just hear those as movement within the sound. The older alternatives to Equal (mean tone, Werckmeister, Kirnberger, and others) smooth out the ratios more selectively. So some note combinations are less sour, others are more sour. They sound quite spicy if you're not used to them - somewhat out of tune (ironic...) but most people are so used to Equal Temperament anything else sounds exotic. So something like this is of historic interest. These tunings are sometimes used for authentic performances of very old ('early') music, and some old church organs were built with them. It's very rare to find them being used for effect in modern songs. (Does happen, but very unusual.) The best solution is dynamic tuning which takes into account the surrounding notes and shifts pitches a little up and down for the smoothest effect. Choirs and orchestras tend to do this anyway, but making it happen in software is a much harder problem.

thih9 2y ago
About software implementations of dynamic tuning - Logic Pro supports this, under the name “Hermode Tuning” https://support.apple.com/en-gb/guide/logicpro/lgcpa88a63e7/mac https://support.apple.com/en-gb/guide/logicpro/lgcpa88a63e7/... > Hermode Tuning automatically controls the tuning of electronic keyboard instruments (…). It retains the pitch relationship between keys and notes, while correcting the individual notes of electronic instruments, ensuring a high degree of tonal purity. This process makes up to 50 finely graded frequencies available per note, while retaining compatibility with the fixed tuning system of 12 notes per octave. Other DAWs have similar options, e.g. Cubase: https://www.steinberg.help/r/cubase-pro/13.0/en/cubase_nuendo/topics/midi_realtime_parameters_and_effects/midi_realtime_parameters_midi_modifiers_hermode_tuning_r.html https://www.steinberg.help/r/cubase-pro/13.0/en/cubase_nuend...